Former President Barack Obama is said to be "furious" about President Donald Trump's unproven claim that Obama ordered a surveillance operation on phones at Trump Tower during the 2016 election.

People close to Obama told The Wall Street Journal in a story published Tuesday night that Obama was "livid" about Trump's unfounded accusations, which came in a series of tweets early Saturday morning.

Obama said before he left office that he would not respond to every controversial thing Trump tweeted, but during his last press conference as commander-in-chief, Obama said he would "examine it when it comes" if there are issues that "go to core questions about our values and our ideals."

RELATED: President Trump accuses Obama on Twitter of wiretapping him

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President Trump accuses Obama on Twitter of wiretapping him

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President Trump accuses Obama on Twitter of wiretapping him

Terrible! Just found out that Obama had my "wires tapped" in Trump Tower just before the victory. Nothing found. This is McCarthyism!

Is it legal for a sitting President to be "wire tapping" a race for president prior to an election? Turned down by court earlier. A NEW LOW!

I'd bet a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to Election!

How low has President Obama gone to tapp my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!

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Trump's explosive accusations — which he made without evidence — appeared to do just that, according to The Journal's Carol E. Lee and Peter Nicholas, who cited people familiar with Obama's thinking who said Trump's tweets about wiretapping undermined "the integrity of the office of the president and Mr. Obama himself."

It is the closest glimpse at Obama's thinking about the allegations after several former members of his administration sought to knock down Trump's claims during interviews on Sunday. The relationship between the 44th and 45th president has been tenuous at best following Trump's election victory in November. The two met at the White House and spoke regularly until they parted ways after Trump's inauguration.

According to The Journal, they have not spoken since. Trump called Obama to thank him for the letter he left for Trump at the White House, the newspaper said. The call went unanswered, ostensibly because of Obama's post-presidency vacation.

FBI Director James Comey and former director of national intelligence James Clapper have both denied that any order for wiretapping was requested or issued, The Journal said, and several White House staffers declined to explain what prompted Trump to make the accusations.

A Tuesday night New York Times report said that Trump "sounded uncertain" hours after his tweets were published on Saturday about how wiretapping at Trump Tower could actually be done. The newspaper said Trump asked some aides whether an investigator "outside the government" could back up his claims.